WEEK 13: Three-phase Calculations and Measurements

Star Connection
Figure 1		Figure 2
Figure 1 shows three loads connected in the star formation to a three phase four wire supply system. Figure 2 shows the phasor diagram, the red to neutral voltage URN is taken as reference and the phase sequence is red, yellow, blue so that the other line to neutral voltages or phase voltages lie as shown.
If URN = UYN = UBN and they are equally spaced the system of voltage is balanced.
Let UL be the voltage between any pair of lines (the line voltage) and UP = URN = UYN = UBN (the phase voltage)
Then UL = 3UP
and IL = IP
where IL is the current in any line and IP is the current in any load or phase. The power per phase is P = UPIPcosØ and the total power is the sum of the amount of power in each phase
If the currents are equal and the phase angles are the same as in figure 3 the load on the system is balanced, the current in the neutral is zero and the total power is
P = 3UL IL cosØ
Figure 3
Delta Connections
Figure 4		Figure 5
Figure 4 shows three loads connected in the delta or mesh formation to a three phase supply system. Figure 5 shows the phasor diagram of the line voltages with the red to yellow voltage taken as reference.
The voltage applied to any load is the line voltage UL and the line current is the phasor difference between the currents in the two loads connected to that line. If the load currents are all equal and make equal phase angles with their respective voltages the system is balanced and
IL = 3IP
The total power under these conditions is
P = 3UL IL cosØ